An empirical analysis and stochastic modelling of aggregate demand behaviour in a spare parts inventory system

The focus of the work here was an empirical analysis of the aggregate independent demand behaviour for spare parts inventories, principally in the automotive industry. In particular, using the pioneering work of RG Brown (1959), who showed that inventory usage values are often log normally distributed, we set out and developed models that go some considerable way to explaining the underlying stochastic basis for this phenomena, why it occurs and some limiting conditions. The justification for this approach was on the grounds that by providing a more fundamental understanding of the underlying stochastic processes that explain the emergent aggregate demand behaviour, a sound starting point would be provided for developing more sophisticated analytical ways to view an inventory range, as a total entity, for planning and control purposes. The analysis was based on extensive data collected from the DAF Trucks (GB) Ltd. spare parts systems spanning the period 1975 to 1986, together with supporting studies from a number of other systems. The analysis showed that in the systems studied spare parts prices are lognormally distributed and this is most likely to be the result of a stochastic process known as the 'theory of breakage'. Analysis also showed that in the DAF Trucks case aggregated and volumes in very short time periods are distributed as a combined Log Series /Negative Binomial distribution (LSD/NBD). The combined LSD/NBD model of aggregate demand volumes is itself fully explained by a stochastic model known as the Afwedson model, which in turn is derived from more elementary conditions based on the Poisson process. We then demonstrated that if these short period aggregate demand distributions are cumulated period by period they converge to a log normal distribution as the stable long run model of aggregate demand volumes. As a result of the lognormality of prices and volumes the resultant inventory usage values are also log normal. Furthermore from insight into the underlying factors that explain the lognormality we have identified the factors and variables that govern the valueso f the parameterso f the particular log normal models of usage values. - The research protocol used in this work incorporated the law verifying process know as 'retroduction' after work and discussions of Uji Ijiri and Herbert Simon (1977); and to a lesser extent we utilised simulation for validation and verification of the derived models. From the proven log normality of demand volumes and usage values we have demonstrated that a number of related key inventory factors are also lognormal, in particular inventory- item turnover rates. Furthermore our conclusions show that some standard inventory performance measures, such as the inventory wide 'stock turnover rate' and the 'stock to sales' ratio, are poor measures to use in the case of highly skewed inventory variables. Finally we have suggested several potentially fruitful areas for developing improved methods of monitoring inventory performance in a variety of circumstances

The role of visual adaptation in cichlid fish speciation

D. Shane Wright (1) , Ole Seehausen (2), Ton G.G. Groothuis (1), Martine E. Maan (1) (1) University of Groningen; GELIFES; EGDB(2) Department of Fish Ecology & Evolution, EAWAG Centre for Ecology, Evolution and Biogeochemistry, Kastanienbaum AND Institute of Ecology and Evolution, Aquatic Ecology, University of Bern.In less than 15,000 years, Lake Victoria cichlid fishes have radiated into as many as 500 different species. Ecological and sexual sel ection are thought to contribute to this ongoing speciation process, but genetic differentiation remains low. However, recent work in visual pigment genes, opsins, has shown more diversity. Unlike neighboring Lakes Malawi and Tanganyika, Lake Victoria is highly turbid, resulting in a long wavelength shift in the light spectrum with increasing depth, providing an environmental gradient for exploring divergent coevolution in sensory systems and colour signals via sensory drive. Pundamilia pundamila and Pundamilia nyererei are two sympatric species found at rocky islands across southern portions of Lake Victoria, differing in male colouration and the depth they reside. Previous work has shown species differentiation in colour discrimination, corresponding to divergent female preferences for conspecific male colouration. A mechanistic link between colour vision and preference would provide a rapid route to reproductive isolation between divergently adapting populations. This link is tested by experimental manip ulation of colour vision - raising both species and their hybrids under light conditions mimicking shallow and deep habitats. We quantify the expression of retinal opsins and test behaviours important for speciation: mate choice, habitat preference, and fo raging performance

Analysis of evaporative flux data for various climates

Estimation of evapotranspiration is a key requirement of hydrologic balance studies and climate analysis. The study reported involved collection of precise weighing lysimeter and meteorological data from three sites representing distinct climates. The combined data set for daily amounts of evapotranspiration and meteorological variables covers a total of 19 years on either an annual or growing season basis. The pan evaporation, Priestley-Taylor, original Penman, and Penman-Monteith evapotranspiration estimating methods arc compared with lysimeter measurements using a moving average of 1-30 days. The results indicate the applicability of the various methods as a function of climate regime and the reduction in standard error of the estimate and increase in the coefficient of determination as a function of length of the moving average period. The results can be used both to determine which methods are most applicable for different climates and the expected magnitude of the error as a function of the estimating interval. This study indicates that a 5-10-day moving average can reduce the standard error of the estimate and increase the coefficient of determination significantly between estimated and measured reference evapotranspiration for several estimating methods for various climates

A mixed methods evaluation of the acceptability of therapy using LEGO® bricks (LEGO® based therapy) in mainstream primary and secondary education

Many autistic children and young people need extra support with social skills. Social skills programmes, such as LEGO® based therapy (LBT), are commonly used to help with these difficulties. The aim of this study was to examine the acceptability of LBT using qualitative interviews and questionnaires with facilitators and parents/guardians on behalf of autistic children and young people. Acceptability was measured in line with constructs of the Theoretical Framework of Acceptability. Questionnaires were analyzed descriptively and between group comparisons were undertaken using the Mann–Whitney U Test. Telephone interviews were undertaken with a sub-sample of facilitators. All interviews were recorded, transcribed verbatim, and framework analysis was performed by two researchers supported by NVivo. The questionnaire response rate was 80% for facilitators and 77% for parents/guardians. Overall acceptability, measured on a 1–5 (minimum–maximum) scale, was high for both facilitators and parents/guardians with a median (range) of 5 (4–5) and 4 (3–5), respectively. Facilitators rated the acceptability of the programme significantly higher overall than parents (p < 0.001). Facilitators reported that participants and wider school staff viewed the programme positively. They observed improvements in communication and social skills during the sessions. Potential barriers to programme delivery, such as resources and staff schedules, were identified but facilitators reported that these challenges did not outweigh the benefits. There is increasing emphasis on the role of schools in seeking to improve social outcomes for autistic children therefore this high degree of acceptability makes this an attractive school-based programme for schools, autistic children and their families

Cladoceran birth and death rates estimates

I. Birth and death rates of natural cladoceran populations cannot be measured directly. Estimates of these population parameters must be calculated using methods that make assumptions about the form of population growth. These methods generally assume that the population has a stable age distribution. 2. To assess the effect of variable age distributions, we tested six egg ratio methods for estimating birth and death rates with data from thirty-seven laboratory populations of Daphnia pulicaria. The populations were grown under constant conditions, but the initial age distributions and egg ratios of the populations varied. Actual death rates were virtually zero, so the difference between the estimated and actual death rates measured the error in both birth and death rate estimates. 3. The results demonstrate that unstable population structures may produce large errors in the birth and death rates estimated by any of these methods. Among the methods tested, Taylor and Slatkin's formula and Paloheimo's formula were most reliable for the experimental data. 4. Further analyses of three of the methods were made using computer simulations of growth of age-structured populations with initially unstable age distributions. These analyses show that the time interval between sampling strongly influences the reliability of birth and death rate estimates. At a sampling interval of 2.5 days (equal to the duration of the egg stage), Paloheimo's formula was most accurate. At longer intervals (7.5–10 days), Taylor and Slatkin's formula which includes information on population structure was most accurate

Measurement of the Proton and Deuteron Spin Structure Functions g2 and Asymmetry A2

We have measured the spin structure functions g2p and g2d and the virtual photon asymmetries A2p and A2d over the kinematic range 0.02 < x < 0.8 and 1.0 < Q^2 < 30(GeV/c)^2 by scattering 38.8 GeV longitudinally polarized electrons from transversely polarized NH3 and 6LiD targets.The absolute value of A2 is significantly smaller than the sqrt{R} positivity limit over the measured range, while g2 is consistent with the twist-2 Wandzura-Wilczek calculation. We obtain results for the twist-3 reduced matrix elements d2p, d2d and d2n. The Burkhardt-Cottingham sum rule integral - int(g2(x)dx) is reported for the range 0.02 < x < 0.8.Comment: 12 pages, 4 figures, 1 tabl

Extension of Earth-Moon libration point orbits with solar sail propulsion

This paper presents families of libration point orbits in the Earth-Moon system that originate from complementing the classical circular restricted three-body problem with a solar sail. Through the use of a differential correction scheme in combination with a continuation on the solar sail induced acceleration, families of Lyapunov, halo, vertical Lyapunov, Earth-centred, and distant retrograde orbits are created. As the solar sail circular restricted three-body problem is non-autonomous, a constraint defined within the differential correction scheme ensures that all orbits are periodic with the Sun’s motion around the Earth-Moon system. The continuation method then starts from a classical libration point orbit with a suitable period and increases the solar sail acceleration magnitude to obtain families of orbits that are parametrised by this acceleration. Furthermore, different solar sail steering laws are considered (both in-plane and out-of-plane, and either fixed in the synodic frame or fixed with respect to the direction of sunlight), adding to the wealth of families of solar sail enabled libration point orbits presented. Finally, the linear stability properties of the generated orbits are investigated to assess the need for active orbital control. It is shown that the solar sail induced acceleration can have a positive effect on the stability of some orbit families, especially those at the L2 point, but that it most often (further) destabilises the orbit. Active control will therefore be needed to ensure long-term survivability of these orbits

Measurements of the Q2Q^2-Dependence of the Proton and Neutron Spin Structure Functions g1p and g1n

The structure functions g1p and g1n have been measured over the range 0.014 < x < 0.9 and 1 < Q2 < 40 GeV2 using deep-inelastic scattering of 48 GeV longitudinally polarized electrons from polarized protons and deuterons. We find that the Q2 dependence of g1p (g1n) at fixed x is very similar to that of the spin-averaged structure function F1p (F1n). From a NLO QCD fit to all available data we find $\Gamma_1^p - \Gamma_1^n =0.176 \pm 0.003 \pm 0.007$ at Q2=5 GeV2, in agreement with the Bjorken sum rule prediction of 0.182 \pm 0.005.Comment: 17 pages, 3 figures. Submitted to Physics Letters